1. Chapter 18. Heat Transfer A PowerPoint Presentation by
Paul E. Tippens, Professor of Physics
Southern Polytechnic State University
© 2007

2. TRANSFER OF HEAT is minimized by multiple layers of beta cloth
TRANSFER OF HEAT is minimized by multiple layers of beta cloth. These and other insulating materials protect spacecraft from hostile environmental conditions. (NASA)

3. Objectives: After finishing this unit, you should be able to:
Demonstrate your understanding of conduction, convection, and radiation, and give examples.
Solve thermal conductivity problems based on quantity of heat, length of path, temperature, area, and time.
Solve problems involving the rate of radiation and emissivity of surfaces.

4. Heat Transfer by Conduction
Conduction is the process by which heat energy is transferred by adjacent molecular collisions inside a material. The medium itself does not move.
Conduction
Direction
From hot to cold.

5. Heat Transfer by Convection
Convection is the process by which heat energy is transferred by the actual mass motion of a heated fluid.
Heated fluid rises and is then replaced by cooler fluid, producing convection currents.
Convection
Convection is significantly affected by geometry of heated surfaces. (wall, ceiling, floor)

6. Heat Transfer by Radiation
Radiation is the process by which heat energy is transferred by electromagnetic waves.
Radiation
Sun
Atomic
No medium is required !

7. Kinds of Heat Transfer
Consider the operation of a typical coffee maker:
Think about how heat is transferred by:
Conduction?
Convection?
Radiation?

8. Heat Current
The heat current H is defined as the quantity of heat Q transferred per unit of time t in the direction from high temperature to low temperature.
Steam
Ice
Typical units are: J/s, cal/s, and Btu/h

9. Thermal Conductivity t1 t2
Dt = t2 - t1
The thermal conductivity k of a material is a measure of its ability to conduct heat.
H = Heat current (J/s)
A = Surface area (m2)
Dt = Temperature difference
L = Thickness of material

10. The SI Units for Conductivity
Hot
Cold
For Copper: k = 385 J/s m C0
Taken literally, this means that for a 1-m length of copper whose cross section is 1 m2 and whose end points differ in temperature by 1 C0, heat will be conducted at the rate of 1 J/s.
In SI units, typically small measures for length L and area A must be converted to meters and square meters, respectively, before substitution into formulas.

11. Older Units for Conductivity
Dt = 1 F0
L = 1 in.
A=1 ft2
Q=1 Btu
t = 1 h
Older units, still active, use common measurements for area in ft2 time in hours, length in seconds, and quantity of heat in Btu’s.
Glass k = 5.6 Btu in./ft2h F0
Taken literally, this means that for a 1-in. thick plate of glass whose area is 1 ft2 and whose sides differ in temperature by 1 F0, heat will be conducted at the rate of 5.6 Btu/h.

12. Thermal Conductivities
Examples of the two systems of units used for thermal conductivities of materials are given below:
Material
Copper:
385
2660
Concrete or Glass:
0.800
5.6
0.040
0.30
Corkboard:

13. Examples of Thermal Conductivity
Comparison of Heat Currents for Similar Conditions: L = 1 cm (0.39 in.); A = 1 m2 (10.8 ft2); Dt = 100 C0
2050 kJ/s
4980 Btu/h
Aluminum:
3850 kJ/s
9360 Btu/h
Copper:
Concrete or Glass:
8.00 kJ/s
19.4 Btu/h
0.400 kJ/s
9.72 Btu/h
Corkboard:

14. Example 1: A large glass window measures 2 m wide and 6 m high
Example 1: A large glass window measures 2 m wide and 6 m high. The inside surface is at 200C and the outside surface is at 120C. How many joules of heat pass through this window in one hour? Assume L = 1.5 cm and that k = 0.8 J/s m C0.
A = (2 m)(6 m) = 12 m2
200C
120C
Dt = t2 - t1 = 8 C0
0.015 m A
Q = ?
t = 1 h
Q = 18.4 MJ

15. Example 2: The wall of a freezing plant is composed of 8 cm of corkboard and 12 cm of solid concrete. The inside surface is at C and the outside surface is +250C. What is the interface temperature ti? ti
250C
-200C HA
8 cm 12 cm
Steady Flow
Note:

16. Rearranging factors gives:
Example 2 (Cont.): Finding the interface temperature for a composite wall. ti
250C
-200C HA
8 cm 12 cm
Steady Flow
Rearranging factors gives:

17. Example 2 (Cont.): Simplifying, we obtain:ti
250C
-200C HA
8 cm 12 cm
Steady Flow
0.075ti C = 250C - ti
From which:
ti = 21.90C
Knowing the interface temperature ti allows us to determine the rate of heat flow per unit of area, H/A.
The quantity H/A is same for cork or concrete:

18. Example 2 (Cont.): Constant steady state flow.
Over time H/A is constant so different k’s cause different Dt’s ti
250C
-200C HA
8 cm 12 cm
Steady Flow
Cork: Dt = 21.90C - (-200C) = 41.9 C0
Concrete: Dt = 250C C = 3.1 C0
Since H/A is the same, let’s just choose concrete alone:

19. Example 2 (Cont.): Constant steady state flow.ti
250C
-200C HA
8 cm 12 cm
Steady Flow
Cork: Dt = 21.90C - (-200C) = 41.9 C0
Concrete: Dt = 250C C = 3.1 C0
Note that 20.7 Joules of heat per second pass through the composite wall. However, the temperature interval between the faces of the cork is 13.5 times as large as for the concrete faces.
If A = 10 m2, the heat flow in 1 h would be ______?
745 kW

20. Radiation
The rate of radiation R is the energy emitted per unit area per unit time (power per unit area).
Rate of Radiation (W/m2):
Emissivity, e : > e > 1
Stefan-Boltzman Constant : s = 5.67 x 10-8 W/m·K4

21. Power Radiated from Surface:
Find Power Radiated
Example 3: A spherical surface 12 cm in radius is heated to 6270C. The emissivity is What power is radiated?
A = m2
T = ; T = 900 K
Power Radiated from Surface:
P = 808 W

22. Summary: Heat Transfer
Conduction: Heat energy is transferred by adjacent molecular collisions inside a material. The medium itself does not move.
Convection is the process by which heat energy is transferred by the actual mass motion of a heated fluid.
Radiation is the process by which heat energy is transferred by electromagnetic waves.

23. Summary of Thermal Conductivity
H = Heat current (J/s)
A = Surface area (m2)
Dt = Temperature difference
L = Thickness of material t1 t2
Dt = t2 - t1
The thermal conductivity k of a material is a measure of its ability to conduct heat.

24. Summary of Radiation
Rate of Radiation (W/m2):
The rate of radiation R is the energy emitted per unit area per unit time (power per unit area).
Emissivity, e : > e > 1
Stefan-Boltzman Constant : s = 5.67 x 10-8 W/m·K4 R

25. Summary of Formulas

26. CONCLUSION: Chapter 18 Transfer of Heat